Consider the model of Section 18.2 with F corresponding to the production function of an individual firm j (with a slight abuse of notation). Let (18.3) correspond to the law of motion of the technology of the firm, with σj = σ(hj ), where hj is the average human capital of the workers of firm j , and σ is a strictly increasing and differentiable function. To simplify the discussion, suppose that each firm employs a single worker.
(a) Derive the wage of the worker of human capital hj.
(b) Show that an increase in g (at any t) increases wages. Derive the implications of changes in g on the returns to human capital. Contrast an increase in the returns to human capital driven by an increase in g with those discussed in Chapter 15.